Abstract

We present an optical quantum random number generator (QRNG) based on the digitized time interval between random photon arrivals. By tailoring the photon flux of the laser diode, the statistics of the waiting-time distribution are altered to approximate the ideal, uniform case. This greatly reduces the need for post-processing, and enables fast, secure quantum random number generation at rates exceeding 110 Mbit/s.

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References

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  1. A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).
  2. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
    [Crossref]
  3. W. Dultz, and E. Hildebrandt, “Optical random-check generator based on the individual photon statistics at the optical beam divider,” PCT Patent WO/98/16008, April 1998.
  4. J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
    [Crossref]
  5. M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
    [Crossref]
  6. N. Lutkenhaus, J. Cohen, and H. Lo, “Efficient use of detectors for random number generation,” U.S. Patent 7197523, March 27, 2007.
  7. P. Kwiat, E. Jeffrey, and J. Altepeter, “Quantum random number generator,” U.S. Patent Application 20060010182, January 12, 2006.
  8. D. L. Snyder, and M. I. Miller, Random Point Processes in Time and Space, (New York, NY: Springer-Verlag, 1991).
  9. E. Ph. D. Jeffrey, Thesis, University of Illinois at Urbana-Champaign, Urbana, IL, 2007.
  10. C. E. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, vol. 27, pp. 379–423 and 623–656, (1948).
  11. A. Rènyi, “On measures of information and entropy,” in Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics, and Probability, 1960, pp. 547–561.
  12. National Institute of Standards and Technology, “A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications,” April 2009. [Online]. Available: http://csrc.nist.gov/publications/nistpubs/800-22-rev1/SP800-22rev1.pdf .
  13. A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
    [Crossref]
  14. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102–024104 (2009).
    [Crossref] [PubMed]

2009 (3)

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[Crossref]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102–024104 (2009).
[Crossref] [PubMed]

2000 (2)

A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
[Crossref]

1994 (1)

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Achleitner, U.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
[Crossref]

Akselrod, G. M.

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

Aviad, Y.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102–024104 (2009).
[Crossref] [PubMed]

Bennett, A. J.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[Crossref]

Dixon, A. R.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[Crossref]

Dynes, J. F.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[Crossref]

Gisin, N.

A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).

Guinnard, L.

A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).

Jeffrey, E. R.

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

Jennewein, T.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
[Crossref]

Kanter, I.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102–024104 (2009).
[Crossref] [PubMed]

Kwiat, P. G.

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

Owens, P. C. M.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Rarity, J. G.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Reidler, I.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102–024104 (2009).
[Crossref] [PubMed]

Rosenbluh, M.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102–024104 (2009).
[Crossref] [PubMed]

Sharpe, A. W.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[Crossref]

Shields, A. J.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[Crossref]

Stefanov, A.

A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).

Tapster, P. R.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Wayne, M. A.

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

Weihs, G.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
[Crossref]

Weinfurter, H.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
[Crossref]

Yuan, Z. L.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[Crossref]

Zbinden, H.

A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).

Zeilinger, A.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
[Crossref]

Appl. Phys. Lett. (1)

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94(23), 231113 (2009).
[Crossref]

J. Mod. Opt. (3)

A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

Phys. Rev. Lett. (1)

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102–024104 (2009).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
[Crossref]

Other (8)

W. Dultz, and E. Hildebrandt, “Optical random-check generator based on the individual photon statistics at the optical beam divider,” PCT Patent WO/98/16008, April 1998.

N. Lutkenhaus, J. Cohen, and H. Lo, “Efficient use of detectors for random number generation,” U.S. Patent 7197523, March 27, 2007.

P. Kwiat, E. Jeffrey, and J. Altepeter, “Quantum random number generator,” U.S. Patent Application 20060010182, January 12, 2006.

D. L. Snyder, and M. I. Miller, Random Point Processes in Time and Space, (New York, NY: Springer-Verlag, 1991).

E. Ph. D. Jeffrey, Thesis, University of Illinois at Urbana-Champaign, Urbana, IL, 2007.

C. E. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, vol. 27, pp. 379–423 and 623–656, (1948).

A. Rènyi, “On measures of information and entropy,” in Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics, and Probability, 1960, pp. 547–561.

National Institute of Standards and Technology, “A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications,” April 2009. [Online]. Available: http://csrc.nist.gov/publications/nistpubs/800-22-rev1/SP800-22rev1.pdf .

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Figures (6)

Fig. 1
Fig. 1

(a) Time intervals between successive registered photons are translated into time-bin values. (b) Data-flow diagram of our previous constant-current implementation [5]. Photons emitted from the laser diode cause the APD to output pulses which are registered by the counter. These counts are then accumulated until enough entropy is present to ‘whiten’ using the SHA-256 hash function. The final data is then output through the PCI bus.

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Fig. 2
Fig. 2

Pre – (a) and Post – (b) processed random data for our previous constant-current QRNG implementation [5]. Red curves are the theoretical expectations for infinite-size data sets. Bias due to the Poissonian nature of our source was compensated for by whitening via the SHA-256 hash function.

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Fig. 4
Fig. 4

Ideal (red) and simulated SPICE (blue) waveforms of the (a) sawtooth, (b) logarithmic converter, and (c) differentiator stages of the pulse-shaping circuit assuming a 50-ns reset period. The delay between pulses is to accommodate the 45-ns deadtime of the APD, and the offset on the final waveform is to keep the laser diode operating above threshold.

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Fig. 5
Fig. 5

(a) Theoretical (red), simulated (blue), and actual current pulse shape. The resulting waiting-time distribution (b) from the final QRNG system has a min-entropy of approximately 0.90 bits per bit; however, when counts outside the dotted line are discarded, resulting in a smaller but more random distribution, the min-entropy increases to 0.9984 bits per bit.

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Fig. 6
Fig. 6

Example of sorted p-values for (red) raw and (blue) whitened random data versus the expected distribution (green). Data from the hash performed better in the approximate entropy test (a) while in the FFT test (b) the unhashed data actually performed better.

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Fig. 3
Fig. 3

Peak min-entropy generation rate vs. reset period T for detector deadtimes of 45 ns (dotted blue), 30 ns (dashed red) and 10 ns (solid green), and time-bin resolution of 100 ps. Optimal trigger periods (denoted by arrows) decrease with deadtime.

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